Converse filed lawsuits against 31 companies in Federal District Court in New York accusing them of trademark infringement on its Chuck Taylor shoe. The brand, owned by Nike Inc., is suing for monetary damages, but is particularly seeking to prevent the continued sale of the alleged infringing product.

Skechers USA, Wal-Mart, Fila, Ed Hardy, K-Mart Corp., Tory Burch, Ralph Lauren Corp., Zulily, Aldo Group, H&M, Highline United and Kitson are among those being sued. Of the 31 companies, four are based in China, two in Canada, one in Australia, one in Italy and one in Japan.

Converse claims the companies are infringing on trademarks that cover the look of the shoe, including the distinctive toecap, toe bumper and side strip as well as the diamond pattern on the bottom of the sole. The Converse star is not in question.

Converse claims look-alike Chuck Taylors have become more common in recent years with their popularity. It claims to have served about 180 cease and desist letters related to the issue since 2008.

It also said it has spent hundreds of millions advertising the shoes, while also acknowledging the iconic brand has benefited from extra publicity reaped from call outs in books, magazines, newspapers, movies and TV shows.

For generations, the Chuck Taylor, universally known as the ‘Chuck, has captured the hearts and minds of millions of consumers, selling over a billion pairs globally during the past century, Converse Chief Executive Officer Jim Calhoun said in the statement. We welcome fair competition, but we do not believe companies have a right to copy the Chucks trademarked look.

The All-Star debuted in 1917 as a basketball shoe and was later renamed the Chuck Taylor.

Sales of Converse reached $1.68 billion in Nike’s fiscal year ended May 31, 2014, up from $1.45 billion in fiscal 2013 and $1.32 million in fiscal 2012. Converse sales were $205.3 million in 2012, the year before Nike acquired the brand for $305 million.